Day 1: What is an Integer?

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Darren Rice
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1 Day 1: What is an Integer? SOL 6.5 The student will identify, represent, order, and compare integers. SOL 6.8 The student will solve multistep consumer-application problems involving fractions and decimals and present data and conclusions in paragraphs, tables, or graphs. Planning a budget will be included. Lesson: The students will create a human number line to identify, compare and order integers. This lesson will include the introduction to their own class checkbook that will incorporate consumer-application with integers. Materials: dice, index cards, checkbook register and checks, Gains and Losses Game Sheet Procedures: 1)Pose the questions, How does the bank know how much money we have in our account? Is it possible to spend more money than you really have in your account? What does it mean to be in the red? 2) Create student checkbook registers with opening balance of $ and write our first check in the amount $14.50 to the school for our lunch account. Chunk 1: 1) Introduce integers as any number represented on the number line. Have students draw a number line. Discuss number line concepts: 1) What happens when you move to the right? 2) What happens when we move to the left? 3) What do the arrows tell you? 4) Does zero always have to be in the middle? 2) Incorporate comparing and ordering integers using the number line. 1) Which is the larger integer 2 or -13? 2) List four integers on the board and have students use the number line to order them from least to greatest and then greatest to least. 3) Human number line. Students will draw an integer from the grab bag of cards and order themselves from least to greatest. Pose questions such as, Who is a greater integer than? We have a student as 4 and a student as -4, what do we notice about these two integers? Chunk 2: 1) Lead students to generate real life situations that match a given integer. 1) For example if you put up -10, students should tell you that represents a loss of ten yards, negative ten degrees, ten dollar debt, ten feet below sea level, etc. 2) If you put up the integer 12, students should tell you they can earn 12 dollars, move 12 spaces ahead on a game board, they can gain 12 pounds, etc. 2) Check thesaurus and research the synonyms for gain and loss. Create a class poster to include all of the words the class finds.

2 Chunk 3: 1) Pair up the students to play version 1 of Gains and Losses. Independent Practice: 1) Students work independently to complete You Don t Say practice worksheet to assess the concepts they learned through playing the game. Closure: 1) Discuss student results from the game. See how many students were in the red. Did anyone come up with a new creative real life situation for positives or negatives to add to our class chart? 2) Draw a checkbook card and record data into checkbook registers. Differentiation: 1) Control and adjust the size of the numbers on the dice given to each pair during the game. Use different kinds of dice to give higher digits to more advanced students. Day 2: Integer Addition and Subtraction SOL 7.5 The student will formulate rules for and solve practical problems involving basic operations (addition, subtraction, multiplication, and division) with integers. SOL 6.8 The student will solve multistep consumer-application problems involving fractions and decimals and present data and conclusions in paragraphs, tables, or graphs. Planning a budget will be included. Lesson: Using two-color counters the students will establish the integer rules for addition and subtraction, including add the opposite and zero pair relationships. Students will be able to incorporate a negative balance into their checkbooks and be able to add and subtract all debits and deposits. Materials: 2 color counters, checkbook registers, Algeblocks Basic Mat Procedures: 1) Continue student checkbook registers by drawing cards and recording data until you reach a negative situation. Discuss how we should note this in our checkbook. Chunk 1: 1) Develop the red counters as negative integers and the yellow counters as positive integers. The red counters only go on the negative side of the mat and the yellow counters only go on the positive side of the mat. 2) Pose the problem 2+5=. Using the positive side, model the 2 yellow counters on the Algeblocks Basic Mat and discuss that addition means that we can add to the mat 5 more yellow counters.

3 3) Pose the problem -2+-5=. Using the negative side, model the 2 red counters on the Algeblocks Basic Mat and discuss that addition means that we can add to the mat 5 more red counters. 4) Draw addition situation practice problems that we just modeled into notes. Formulate the rule for adding two positive integers and adding two negative integers. 1) Example: When you are adding two positive integers you find the sum of the terms and the answer is always positive. Chunk 2: 1) Pose the problem -2+2=. Use counters to teach the concept of zero pairs. Incorporate integer terms from Day 1 and ask students what the -2 could stand for. Use the situation and talk about getting 2 back. Where would you be on the number line? 1) Does removing the zero pair change the value of the mat? 2) Pose the problem -2+5=. Use the counters to model the problem using both sides of the mat. Generate a real life situation that matches the problem and incorporate removing zero pairs. Do multiple examples including, 2+-5 and -5+2 until students develop the rule for adding integers with unlike signs. 1) Does removing the zero pair change the value of the mat? 2) Do we need to add more zero pairs? 3) Draw addition situation practice problems that we just modeled into notes. Formulate the rule for adding integers with different signs. 1) Example: When the signs are different you subtract and take the sign of the larger term. Independent Practice: 1) Students work independently to complete Adding Integers practice worksheet. Closure: 1) Watch Math 6 Spy Guys lesson: Understanding Integers. 2) Draw a checkbook card and record data. Differentiation: 1) Students may continue to use the 2 color counters and mat to complete independent practice.

4 Day 3: Integer Subtraction SOL 7.5 The student will formulate rules for and solve practical problems involving basic operations (addition, subtraction, multiplication, and division) with integers. SOL 6.8 The student will solve multistep consumer-application problems involving fractions and decimals and present data and conclusions in paragraphs, tables, or graphs. Planning a budget will be included. Lesson: Using two-color counters the students will establish the integer rules for subtraction, including add the opposite and zero pair relationships. Students will be able to incorporate a negative balance into their checkbooks and be able to add and subtract all debits and deposits. Materials: 2 color counters, checkbook registers, Algeblocks Basic Mat, dice, Gains and Losses game sheet. Procedures: 1) Continue student checkbook registers by drawing cards and recording data. Chunk 1: 1) Review the red counters as negative integers and the yellow counters as positive integers. The red counters only go on the negative side of the mat and the yellow counters only go on the positive side of the mat. 2) Pose the problem 5-2=. Using the positive side, model the 5 yellow counters on the Algeblocks Basic Mat and discuss that subtraction means that we must take away 2 yellow counters. 3) Pose the problem 2-5=. Using the positive side, model the 2 yellow counters on the Algeblocks Basic Mat and discuss that subtraction means that we must take away 5 yellow counters. 1) Can we do that? 2) What strategy can we use to get some more yellow counters on our mat? 3) Incorporate adding in zero pairs. 4) Continue developing the rule with multiple examples until students are confident. 5) Have students generate real life situations to match the equations you are modeling. 4) Draw subtraction situation practice problems that we just modeled into notes. Formulate the rule for subtracting integers. 1) Example: Add the opposite and follow rules for addition. Chunk 2: 1) Work with a partner to complete Subtracting Integers practice worksheet. Allow students to continue using their 2 color counters until they master the concept of the rule. Have students circle the problem where they stopped using the counters for teacher assessment.

5 Chunk 3: 1) Pair up the students to play version 2 of Gains and Losses. Independent Practice: 1) Students work independently to complete Integer sums and Differences practice worksheet. Closure: 1) Watch Brain Pop: Integer Operations 2) Draw a checkbook card and record data. Differentiation: 1) Students may continue to use the 2 color counters and mat to complete independent practice. 2) Control and adjust the size of the numbers on the dice given to each pair during the game. Use different kinds of dice to give higher digits to more advanced students. Day 4: Hands on Equations SOL 6.23 The student will a) model and solve algebraic equations, using concrete materials; b) solve one-step linear equations in one variable, involving whole number coefficients and positive rational solutions; and c) use the following algebraic terms appropriately: variable, coefficient, term, and equation. SOL 7.22 The student will a) solve one-step linear equations and inequalities in one variable with strategies involving inverse operations and integers, using concrete materials, pictorial representations, and paper and pencil; and b) solve practical problems requiring the solution of a one-step linear equation. Lesson: Students will establish the inverse operations and solve one step equations using Hands on Equations. Students will then turn pictorial representations into one-step equations. Checkbook entries will continue to enforce addition and subtraction of integers. Materials: Hands on Equations Kit, copies of the balance scale mats, checkbook registers and checks. Procedures: 1) Continue student checkbook idea. Tell students that they have extra money in their account but we only know their new balance! I made a deposit yesterday and forgot to record it in the register. How can we find out how much the deposit was?

6 Chunk 1: 1) Introduce and discuss the concept of a variable and how to use it in a problem. Develop how to write an equation using a variable. 2) Introduce the game pieces of the Hands on Equation Kit and discuss the concept of a balance scale and legal moves. 3) Model x+4=7. Discuss how to use the inverse operation of addition to take away 4 from each side. 4) Continue to practice problems and model solutions to classroom lesson sheets from the kit. 5) Draw visual representations to show solutions to the equations we just solved. Chunk 2: 1) Model x 4 = 7. Discuss how to use the inverse operation of subtraction to add 4 to each side. 2) Continue to practice problems and model solutions to classroom lesson sheets from the kit. 3) Draw visual representations to show solutions to the equations we just solved. 4) Continue to practice problems and model solutions to classroom lesson sheets from the kit. Chunk 3: 1) Using their pictorial representations show how to solve the equations in pencil and paper format. Continue to reinforce the concept of doing the same thing to both sides. 1) Example: x 4 = 7 x = x = 11 Independent Practice: 1) Students work independently to complete Addition and Subtraction Equations practice worksheet. Closure: 1) Return to classroom checkbook. Write the addition problem as an equation and show how we use the inverse operation to solve for x. Differentiation: 1) Students may continue to use the game pieces to solve equations. 2) Students may use their calculators to solve operations problems. Created by Kristin Dewald and Ann Huffman

7 Day 5: Creating Word Problems SOL 6.23 The student will a) model and solve algebraic equations, using concrete materials; b) solve one-step linear equations in one variable, involving whole number coefficients and positive rational solutions; and c) use the following algebraic terms appropriately: variable, coefficient, term, and equation. SOL 7.22 The student will a) solve one-step linear equations and inequalities in one variable with strategies involving inverse operations and integers, using concrete materials, pictorial representations, and paper and pencil; and b) solve practical problems requiring the solution of a one-step linear equation. Lesson: Word problems will be created from pictorial representations and solved using integer operations and one-step equations. Students will make their final checkbook entries and quiz on their checkbook register. Materials: white drawing paper, coloring supplies and checkbook registers and checks Procedures: 1) Complete student checkbook. Analyze the checkbook register and review the entries, process, check writing, debits and deposits we have made this week. Chunk 1: 1) Quiz on Checkbook Register Entries. 1) Project dogs and bones picture for the students to examine. Students will generate a word problem as a class to match the picture. Write the equation to match our word problem and solve completely. 2) Project happy meal picture for the students to examine. Students will generate a word problem as a class to match the picture. Write the equation to match our word problem and solve completely. Chunk 2: 1) Allow students 15 minutes to create a drawing of any kind. Explain that they will use their drawing to generate a word problem. Remind students they can use the class poster for gains and losses synonyms to help them be more creative. 2) Students will generate a word problem to match their picture. Write the word problem on the poster below their picture. 3) Underneath all of their work, students will write the equation needed to solve their word problem and show the solution.

8 Closure: 1) Students will take turns sharing their pictures. Allow them to ask for possible word problem scenarios from classmates before sharing their own. Differentiation: 1) Have clip art available for students to cut and paste. 2) Classroom gains and losses poster can be made into a handout. Created by Kristin Dewald and Ann Huffman

9 Created by Kristin Dewald and Ann Huffman

10 Created by Kristin Dewald and Ann Huffman

Mathematics Success Level E

Mathematics Success Level E T403 [OBJECTIVE] The student will generate two patterns given two rules and identify the relationship between corresponding terms, generate ordered pairs, and graph the ordered pairs on a coordinate plane.